U.S. patent application number 13/206558 was filed with the patent office on 2013-02-14 for cutting inserts and cutting tool systems having sinusoidal and helical cutting edges.
This patent application is currently assigned to TDY Industries, Inc.. The applicant listed for this patent is Jean-Luc Dufour, X. Daniel Fang, Frederick John Palmer, David J. Wills. Invention is credited to Jean-Luc Dufour, X. Daniel Fang, Frederick John Palmer, David J. Wills.
Application Number | 20130039705 13/206558 |
Document ID | / |
Family ID | 46650871 |
Filed Date | 2013-02-14 |
United States Patent
Application |
20130039705 |
Kind Code |
A1 |
Fang; X. Daniel ; et
al. |
February 14, 2013 |
CUTTING INSERTS AND CUTTING TOOL SYSTEMS HAVING SINUSOIDAL AND
HELICAL CUTTING EDGES
Abstract
A cutting tool system is designed to have a combined
sinusoidal-shaped and helical-shaped cutting edge formed by an
assembly of aligned common cutting inserts each having a sinusoidal
and helical cutting edge.
Inventors: |
Fang; X. Daniel; (Brentwood,
TN) ; Palmer; Frederick John; (Warwickshire, GB)
; Dufour; Jean-Luc; (Franklin, TN) ; Wills; David
J.; (Franklin, TN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Fang; X. Daniel
Palmer; Frederick John
Dufour; Jean-Luc
Wills; David J. |
Brentwood
Warwickshire
Franklin
Franklin |
TN
TN
TN |
US
GB
US
US |
|
|
Assignee: |
TDY Industries, Inc.
Pittsburgh
PA
|
Family ID: |
46650871 |
Appl. No.: |
13/206558 |
Filed: |
August 10, 2011 |
Current U.S.
Class: |
407/42 ;
29/428 |
Current CPC
Class: |
Y10T 407/1924 20150115;
Y10T 407/23 20150115; B23C 5/207 20130101; Y10T 29/49826 20150115;
Y10T 407/1962 20150115; B23C 5/02 20130101; B23C 5/109 20130101;
B23C 2200/206 20130101; Y10T 407/1966 20150115; B23P 15/34
20130101 |
Class at
Publication: |
407/42 ;
29/428 |
International
Class: |
B23C 5/20 20060101
B23C005/20; B23P 15/34 20060101 B23P015/34; B23C 5/10 20060101
B23C005/10 |
Claims
1. A cutting tool system comprising: a tool holder comprising a
plurality of common insert pockets positioned in a helical
orientation about a longitudinal axis of the tool holder; and a
plurality of common cutting inserts removably attachable to the
plurality of common insert pockets in the tool holder to form at
least one cutting flute on the tool holder, the at least one
cutting flute comprising a helical grouping of common cutting
inserts positioned in the insert pockets; wherein the common
cutting inserts each comprise at least one sinusoidal and helical
cutting edge; and wherein the at least one cutting flute comprises
a sinusoidal and helical cutting edge positioned about the
longitudinal axis of the tool holder and formed by alignment of the
individual sinusoidal and helical cutting edges of the common
cutting inserts that comprise the at least one cutting flute.
2. The cutting tool system of claim 1, wherein the at least one
sinusoidal and helical cutting edge of the common cutting inserts
comprises a shape comprising one sinusoidal wavelength.
3. The cutting tool system of claim 1, wherein the common cutting
inserts each comprise two or more sinusoidal and helical cutting
edges that are indexable in the insert pockets.
4. The cutting tool system of claim 1, wherein the common cutting
inserts each comprise two sinusoidal and helical cutting edges that
are indexable in the insert pockets.
5. The cutting tool system of claim 1, wherein the common cutting
inserts each comprise four sinusoidal and helical cutting edges
that are indexable in the insert pockets.
6. The cutting tool system of claim 1, further comprising an
end-face cutting insert removably attachable to an insert pocket
positioned at an engaging end of the tool holder, the end-face
cutting insert having a shape that is different than a shape of the
plurality of common cutting inserts.
7. The cutting tool system of claim 6, wherein the end-face cutting
insert comprises a helical cutting edge that helically aligns with
the sinusoidal and helical cutting edges of the plurality of common
cutting inserts forming the sinusoidal and helical cutting edge of
the at least one cutting flute.
8. The cutting tool system of claim 6, wherein the end-face cutting
insert comprises a sinusoidal and helical cutting edge that
helically aligns with the sinusoidal and helical cutting edges of
the plurality of common cutting inserts forming the sinusoidal and
helical cutting edge of the at least one cutting flute.
9. A cutting tool system comprising: a tool holder comprising two
or more series of common insert pockets, each series of common
insert pockets positioned in a helical orientation about a
longitudinal axis of the tool holder; and a plurality of common
cutting inserts removably attachable to the common insert pockets
in the tool holder to form two or more cutting flutes on the tool
holder, the two or more cutting flutes each comprising a helical
grouping of the common cutting inserts positioned in the insert
pockets; wherein the common cutting inserts each comprise at least
one sinusoidal and helical cutting edge; and wherein the two or
more cutting flutes each comprise a sinusoidal and helical cutting
edge positioned about the longitudinal axis of the tool holder and
formed by alignment of the individual sinusoidal and helical
cutting edges of the common cutting inserts that comprise the two
or more cutting flutes.
10. The cutting tool system of claim 9, wherein the at least one
sinusoidal and helical cutting edge of the common cutting inserts
comprises a shape comprising one sinusoidal wavelength.
11. The cutting tool system of claim 9, wherein the common cutting
inserts each comprise two or more sinusoidal and helical cutting
edges that are indexable in the insert pockets.
12. The cutting tool system of claim 9, wherein the common cutting
inserts each comprise two sinusoidal and helical cutting edges that
are indexable in the insert pockets.
13. The cutting tool system of claim 9, wherein the common cutting
inserts each comprise four sinusoidal and helical cutting edges
that are indexable in the insert pockets.
14. The cutting tool system of claim 9, wherein adjacent helical
groupings of the common cutting inserts are offset relative to each
other along the longitudinal axis of the tool holder so that the
inserts comprising adjacent helical flutes are not longitudinally
aligned in a cross sectional plane perpendicular to the
longitudinal axis.
15. The cutting tool system of claim 9, further comprising two or
more end-face cutting inserts, each end-face cutting insert being
removably attachable to an insert pocket positioned at an engaging
end of the tool holder helically aligned with one of the two or
more series of common insert pockets, and each end-face cutting
insert having a shape that is different than a shape of the
plurality of common cutting inserts.
16. The cutting tool system of claim 15, wherein the two or more
end-face cutting inserts each comprise a helical cutting edge that
helically aligns with the sinusoidal and helical cutting edges of
the plurality of common cutting inserts forming the sinusoidal and
helical cutting edges of the two or more cutting flutes.
17. The cutting tool system of claim 15, wherein the two or more
end-face cutting inserts each comprise a sinusoidal and helical
cutting edge that helically aligns with the sinusoidal and helical
cutting edges of the plurality of common cutting inserts forming
the sinusoidal and helical cutting edges of the two or more cutting
flutes.
18. The cutting tool system of claim 15, wherein the two or more
end-face cutting inserts have the same shape, are differently
sized, and are positioned in respective insert pockets with a
common longitudinal clearance, so that adjacent helical groupings
of the common cutting inserts are offset relative to each other
along the longitudinal axis of the tool holder so that the inserts
comprising adjacent helical flutes are not longitudinally aligned
in a cross sectional plane perpendicular to the longitudinal
axis.
19. A cutting insert comprising at least one sinusoidal and helical
cutting edge.
20. The cutting insert of claim 19, wherein the at least one
sinusoidal and helical cutting edge comprises a shape comprising
one sinusoidal wavelength.
21. The cutting insert of claim 19, wherein the cutting insert
comprises two or more sinusoidal and helical cutting edges.
22. The cutting insert of claim 19, wherein the cutting insert
comprises two sinusoidal and helical cutting edges.
23. The cutting insert of claim 19, wherein the cutting insert
comprises four sinusoidal and helical cutting edges.
24. A method for producing a cutting tool system comprising: a tool
holder comprising a plurality of common insert pockets positioned
in a helical orientation about a longitudinal axis of the tool
holder; and a plurality of common cutting inserts removably
attachable to the plurality of common insert pockets in the tool
holder to form at least one cutting flute on the tool holder, the
at least one cutting flute comprising a helical grouping of common
cutting inserts positioned in the insert pockets; wherein the
common cutting inserts each comprise at least one sinusoidal and
helical cutting edge; the method comprising: positioning a cutting
insert having a sinusoidal-shaped cutting edge as if it were on the
tool holder with a helix angle; and modifying the sinusoidal shape
of the cutting edge of the cutting insert to coincide with a
cylindrical surface defined by a cutting radius centered at a
cutting axis of the cutting tool system.
25. The method of claim 24, further comprising: positioning a first
common cutting insert having a sinusoidal-shaped cutting edge as if
it were on a tool holder with a helix angle; positioning a second
common cutting insert having a sinusoidal-shaped cutting edge as if
it were on a tool holder with a helix angle; rotating the second
common cutting insert about the cutting axis of the cutting tool
system while maintaining a constant cutting radius defined by the
cutting tool system; and translating the second cutting insert
parallel to the cutting axis while maintaining the constant cutting
radius defined by the cutting tool system.
26. The method of claim 25, further comprising: successively
positioning a plurality of common cutting inserts having a
sinusoidal-shaped cutting edge as if the cutting inserts were on a
tool holder with a helix angle; successively rotating each of the
plurality of common cutting insert about the cutting axis of the
cutting tool system while maintaining the constant cutting radius
defined by the cutting tool system; and successively translating
each of the plurality of cutting inserts parallel to the cutting
axis while maintaining the constant cutting radius defined by the
cutting tool system.
27. The method of claim 24, further comprising: positioning a
seating surface of a first insert pocket according to an assembly
position of the first common cutting insert having a
sinusoidal-shaped cutting edge as if the first cutting insert were
on a tool holder with a helix angle; positioning a seating surface
of a second insert pocket according to an assembly position of the
second common cutting insert having a sinusoidal-shaped cutting
edge as if the second cutting insert were on the tool holder with a
helix angle; rotating the seating surface of the second insert
pocket about the cutting axis of the cutting tool system while
maintaining a constant cutting radius defined by the cutting tool
system; and translating the seating surface of the second insert
pocket parallel to the cutting axis while maintaining the constant
cutting radius defined by the cutting tool system.
28. The method of claim 27, further comprising: positioning seating
surfaces of a plurality of insert pockets according to assembly
positions of a plurality of common cutting inserts having a
sinusoidal-shaped cutting edge as if the plurality of common
cutting inserts were on the tool holder with a helix angle;
successively rotating each of the seating surfaces of the plurality
of insert pockets about the cutting axis of the cutting tool system
while maintaining the constant cutting radius defined by the
cutting tool system; and successively translating each of the
seating surfaces of the plurality of insert pockets parallel to the
cutting axis while maintaining the constant cutting radius defined
by the cutting tool system.
Description
TECHNICAL FIELD
[0001] This disclosure generally relates to cutting tools,
including cutting tool holders and cutting inserts. In particular,
this disclosure relates to indexable and replaceable cutting
inserts and to tool holders configured to engage and secure
indexable and replaceable cutting inserts such as, for example,
inserts and holders for rotary machining tool systems.
BACKGROUND
[0002] Indexable cutting inserts for cutting tools include, for
example, cutting inserts made of carbide, ceramic, coated carbide,
coated ceramic, or other hard materials. Cutting inserts generally
have a unitary structure and one or more cutting edges located at
various corners or around peripheral edges of the inserts.
Indexable cutting inserts are mechanically secured to a tool
holder, but the inserts are adjustable and removable in relation to
the tool holder. Indexable cutting inserts may be readily
re-positioned (i.e., indexed) to present a new cutting edge to
engage a workpiece, or indexable cutting inserts may be replaced in
a tool holder when the cutting edges dull or fracture, for example.
In this manner, indexable insert cutting tools are modular cutting
tool assemblies that include at least one cutting insert and a tool
holder.
[0003] Indexable insert cutting tool systems comprising a tool
holder and one or more replaceable and/or indexable cutting inserts
are generally more economical than unitary cutting tools. This is
so because indexable insert cutting tool systems allow for the
indexing and replacement of worn and/or damaged cutting
edges/surfaces, whereas unitary cutting tools require scrapping the
entire cutting tool when worn out or damaged. However, for rotary
cutting tools that require complex cutting edge configurations
along the longitudinal axis of the tool, such as, for example,
milling and other rotary machining tools, unitary cutting tools are
less complex to design and manufacture than indexable insert
cutting tool systems. This is so because the cutting edge
configuration of an indexable insert cutting tool system must be
formed by an assembly of separate cutting inserts as opposed to a
continuous and unitary piece of shaped material.
SUMMARY
[0004] In a non-limiting embodiment, a cutting insert comprises at
least one sinusoidal and helical cutting edge.
[0005] In another non-limiting embodiment, a cutting tool system
comprises a tool holder and a plurality of common cutting inserts.
The tool holder comprises a plurality of common insert pockets
positioned in a helical orientation about a longitudinal axis of
the tool holder. The plurality of common cutting inserts are
removably attachable to the plurality of common insert pockets in
the tool holder. When so attached, the plurality of common cutting
inserts form at least one cutting flute on the tool holder. The at
least one cutting flute comprises a helical grouping of common
cutting inserts positioned in the insert pockets. The common
cutting inserts each comprise at least one sinusoidal and helical
cutting edge. The at least one cutting flute comprises a sinusoidal
and helical cutting edge positioned about the longitudinal axis of
the tool holder. The sinusoidal and helical cutting edge of the at
least one cutting flute is formed by alignment of the individual
sinusoidal and helical cutting edges of the common cutting inserts
that comprise the at least one cutting flute.
[0006] In another non-limiting embodiment, a cutting tool system
comprises a tool holder and a plurality of common cutting inserts.
The tool holder comprises two or more series of common insert
pockets. Each series of common insert pockets is positioned in a
helical orientation about a longitudinal axis of the tool holder.
The plurality of common cutting inserts are removably attachable to
the common insert pockets in the tool holder. When so attached, the
plurality of common cutting inserts form two or more cutting flutes
on the tool holder. The two or more cutting flutes each comprise a
helical grouping of the common cutting inserts positioned in the
insert pockets. The common cutting inserts each comprise at least
one sinusoidal and helical cutting edge. The two or more cutting
flutes each comprise a sinusoidal and helical cutting edge
positioned about the longitudinal axis of the tool holder. The
sinusoidal and helical cutting edges of the two or more cutting
flutes are formed by alignment of the individual sinusoidal and
helical cutting edges of the common cutting inserts that comprise
the two or more cutting flutes.
[0007] It is understood that the invention disclosed and described
in this specification is not limited to the embodiments summarized
in this Summary.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] Various features and characteristics of the non-limiting and
non-exhaustive embodiments disclosed and described in this
specification may be better understood by reference to the
accompanying figures, in which:
[0009] FIG. 1 is a three-dimensional perspective view of a cutting
insert comprising two indexable cutting edges, each cutting edge
comprising a sinusoidal and helical geometric shape;
[0010] FIG. 2 is an end view of the cutting insert shown in FIG. 1
(viewed from the end shown in perspective in FIG. 1);
[0011] FIG. 3 is a top view, together with two detailed views, of
the cutting insert shown in FIGS. 1 and 2;
[0012] FIG. 4 is a side view of the cutting insert shown in FIGS.
1-3 (viewed from the left side of the cutting insert as shown in
FIG. 3);
[0013] FIG. 5 shows schematic diagrams of the cutting insert shown
in FIGS. 1-4 illustrating the sinusoidal and helical cutting edges
of the cutting insert, in which FIG. 5(a) is a schematic end view
and FIG. 5(b) is a schematic top view;
[0014] FIG. 6 shows schematic diagrams of the cutting insert shown
in FIGS. 1-5 illustrating the geometric positioning of the cutting
insert relative to a coordinate system, positioned as if the
cutting insert were secured on a rotary tool holder (not shown), in
which FIG. 6(a) is a top view schematic diagram and FIGS. 6(b) and
6(c) are perspective view schematic diagrams;
[0015] FIG. 7 shows schematic diagrams illustrating curves derived
to establish a mathematical design model for the sinusoidal and
helical cutting edges of the insert shown in FIGS. 1-6, in which
the curves shown in FIGS. 7(a), 7(b), and 7(c) correspond to the
cutting insert positioning shown in FIGS. 6(a), 6(b), and 6(c),
respectively;
[0016] FIG. 8 shows schematic diagrams illustrating the relative
positioning of a series of common cutting inserts (as shown in
FIGS. 1-6), positioned as if the cutting inserts were assembled and
secured to a rotary tool holder (not shown) to form a cutting flute
comprising the series of cutting inserts and having a cutting edge
comprising a sinusoidal and helical geometric shape, in which FIG.
8(a) is a side view schematic diagram of the cutting flute and FIG.
8(b) is an end view schematic diagram of the cutting flute;
[0017] FIG. 9 shows three views of a cutting insert having two
indexable cutting edges and configured to be used as an end-face
cutting insert in combination with the cutting inserts as shown in
FIGS. 1-6 and 8, in which FIG. 9(a) is a top view of the end
cutting insert, FIG. 9(b) is a view from the direction indicated by
arrow HH in FIG. 9(a), and FIG. 9(c) is a view from the direction
indicated by arrow VV in FIG. 9(a);
[0018] FIG. 10 shows schematic diagrams illustrating the relative
positioning of a series of common cutting inserts (as shown in
FIGS. 1-6 and 8) and a different end-face cutting insert (as shown
in FIG. 9), positioned as if the cutting inserts were assembled and
secured to a rotary tool holder (not shown) to form a cutting flute
comprising the series of common cutting inserts and having a
cutting edge comprising a sinusoidal and helical geometric shape,
in which FIG. 10(a) is a side view schematic diagram of the cutting
flute and FIG. 10(b) is an end view schematic diagram of the
cutting flute;
[0019] FIG. 11 shows schematic diagrams illustrating the relative
positioning of a series of different-sized end-face cutting inserts
(similar to the end-face cutting insert shown in FIG. 9),
positioned as if the end-face cutting inserts where assembled and
secured to a rotary tool holder (not shown) configured to comprise
five cutting flutes, in which FIG. 11(a) is a side view schematic
diagram of the assembly and FIG. 11(b) is an end view schematic
diagram of the assembly;
[0020] FIG. 12 shows schematic views illustrating the relative
positioning of five cutting flutes, each flute comprising a
different-sized end-face cutting insert (as shown in FIGS. 9 and
11) and a series of common cutting inserts (as shown in FIGS. 1-6
and 8), positioned as if the cutting inserts were assembled and
secured to a rotary tool holder (not shown), and each cutting flute
having a cutting edge comprising a sinusoidal and helical geometric
shape, in which FIG. 12(a) is an end view schematic diagram of the
five cutting flutes and FIG. 12(b) is a side view schematic diagram
of the five cutting flutes;
[0021] FIG. 13 shows two views of an indexable insert cutting tool
system comprising a tool holder comprising five cutting flutes,
each cutting flute comprising a different-sized end cutting insert
(as shown in FIGS. 9 and 11) and a series of common cutting inserts
(as shown in FIGS. 1-6 and 8), and each cutting flute having a
cutting edge comprising a sinusoidal and helical geometric shape,
in which FIG. 13(a) is an end view of the cutting tool system and
FIG. 13(b) is a side view of the cutting tool system;
[0022] FIG. 14 shows three views of a cutting insert comprising
four indexable cutting edges, each cutting edge comprising a
sinusoidal and helical geometric shape, in which FIG. 14(a) is a
top view of the cutting insert, FIG. 14(b) is a side view of the
cutting insert, and FIG. 14(c) is a three-dimensional perspective
view of the cutting insert;
[0023] FIG. 15 shows schematic diagrams of the cutting insert shown
in FIG. 14 illustrating the geometrical positioning of the cutting
insert relative to a coordinate system, positioned as if the
cutting insert were secured on a rotary tool holder (not shown), in
which FIG. 15(a) is a side view schematic diagram, FIG. 15(b) is a
top view schematic diagram, and FIG. 15(c) is a perspective view
schematic diagram;
[0024] FIG. 16 shows schematic diagrams illustrating the relative
positioning of a series of common cutting inserts (as shown in
FIGS. 14 and 15), positioned as if the cutting inserts were
assembled and secured to a rotary tool holder (not shown) to form a
cutting flute comprising the series of cutting inserts and having a
cutting edge comprising a sinusoidal and helical geometric shape,
in which FIG. 16(a) is a side view schematic diagram of the cutting
flute and FIG. 16(b) is an end view schematic diagram of the
cutting flute;
[0025] FIG. 17 shows schematic diagrams illustrating the relative
positioning of a common cutting insert having two indexable cutting
edges and a different end-face cutting insert having two indexable
cutting edges, positioned as if the cutting inserts were assembled
and secured to a rotary tool holder (not shown) to form a cutting
flute comprising the cutting inserts and forming a cutting edge
comprising a sinusoidal and helical geometric shape, in which FIG.
17(a) is an end view schematic diagram of the cutting flute and
FIGS. 17(b) and 17(c) are side view schematic diagrams of the
cutting flute;
[0026] FIG. 18 shows two views of a cutting insert comprising two
indexable cutting edges, each cutting edge comprising a sinusoidal
and helical geometric shape, in which FIG. 18(a) is a
three-dimensional perspective view of the cutting insert and FIG.
18(b) is a top view of the cutting insert;
[0027] FIG. 19 shows two views of a cutting insert comprising two
indexable cutting edges, each cutting edge comprising a sinusoidal
and helical geometric shape, in which FIG. 19(a) is a
three-dimensional perspective view of the cutting insert and FIG.
19(b) is a top view of the cutting insert;
[0028] FIG. 20 is a three-dimensional perspective view of a cutting
insert similar to the cutting insert shown in FIGS. 1-6 and 8 and
comprising two indexable sinusoidal and helical cutting edges and
notches positioned along the cutting edges;
[0029] FIG. 21(a) is a schematic diagram illustrating the
positioning of a cutting insert comprising two indexable,
sinusoidal, and helical cutting edges relative to a tool holder and
a coordinate system;
[0030] FIG. 21(b) is a schematic diagram illustrating the
positioning of a series of common cutting inserts comprising two
indexable, sinusoidal, and helical cutting edges relative to a tool
holder and a coordinate system, in which the series of common
cutting inserts form a cutting flute comprising the cutting inserts
and having a cutting edge comprising a sinusoidal and helical
geometric shape; and
[0031] FIG. 22 is a schematic diagram of an embodiment of a
helix.
[0032] The reader will appreciate the foregoing details, as well as
others, upon considering the following detailed description of
various non-limiting and non-exhaustive embodiments according to
this specification.
DESCRIPTION
[0033] Various embodiments are described and illustrated in this
specification to provide an overall understanding of the structure,
function, operation, manufacture, and use of the disclosed cutting
inserts and cutting tool systems. It is understood that the various
embodiments described and illustrated in this specification are
non-limiting and non-exhaustive. Thus, the invention is not
necessarily limited by the description of the various non-limiting
and non-exhaustive embodiments disclosed in this specification. The
features and characteristics illustrated and/or described in
connection with various embodiments may be combined with the
features and characteristics of other embodiments. Such
modifications and variations are intended to be included within the
scope of this specification. As such, the claims may be amended to
recite any features or characteristics expressly or inherently
described in, or otherwise expressly or inherently supported by,
this specification. Further, Applicant(s) reserve the right to
amend the claims to affirmatively disclaim features or
characteristics that may be present in the prior art. Therefore,
any such amendments comply with the requirements of 35 U.S.C.
.sctn.112, first paragraph, and 35 U.S.C. .sctn.132(a). The various
embodiments disclosed and described in this specification can
comprise, consist of, or consist essentially of the features and
characteristics as variously described herein.
[0034] Any patent, publication, or other disclosure material
identified herein is incorporated by reference into this
specification in its entirety unless otherwise indicated, but only
to the extent that the incorporated material does not conflict with
existing description, definitions, statements, or other disclosure
material expressly set forth in this specification. As such, and to
the extent necessary, the express disclosure as set forth in this
specification supersedes any conflicting material incorporated by
reference herein. Any material, or portion thereof, that is said to
be incorporated by reference into this specification, but which
conflicts with existing definitions, statements, or other
disclosure material set forth herein, is only incorporated to the
extent that no conflict arises between that incorporated material
and the existing disclosure material. Applicants reserve the right
to amend this specification to expressly recite any subject matter,
or portion thereof, incorporated by reference herein.
[0035] The grammatical articles "one", "a", "an", and "the", as
used in this specification, are intended to include "at least one"
or "one or more", unless otherwise indicated. Thus, the articles
are used in this specification to refer to one or more than one
(i.e., to "at least one") of the grammatical objects of the
article. By way of example, "a component" means one or more
components, and thus, possibly, more than one component is
contemplated and may be employed or used in an implementation of
the described embodiments. Further, the use of a singular noun
includes the plural, and the use of a plural noun includes the
singular, unless the context of the usage requires otherwise.
[0036] In rotary cutting and machining tools, a helical cutting
edge gradually engages a workpiece to the full length of the
cutting edge, and gradually disengages from the workpiece as
material is cut and removed. The cutting action from a helical
cutting edge results in a smooth cut and evenly distributed
stresses along the cutting edge. In contrast, a straight cutting
edge engages a workpiece along the full length of the cutting edge
at the same time. This abrupt engagement causes a rapid cutting
tooth load, which may cause undesirable vibrations and tool
"chatter."
[0037] However, for cutting tools comprising indexable cutting
inserts, if the arrangement of the multiple cutting inserts
assembled and aligned on the tool holder does not form a continuous
cutting edge having a true helical geometric shape, the modular
cutting tool may create a rough surface finish and/or stepped/wavy
surface topology on the machined surface. It is difficult to
produce a cutting edge having a continuous and true helical
geometric configuration on modular rotary cutting tools comprising
multiple cutting inserts because the length of the cutting edge is
formed by the respective cutting edges of the multiple individual
cutting inserts when assembled in the tool holder.
[0038] The uneven and rough surface topology of a cut made with a
modular rotary cutting tool comprising a cutting flute comprising a
series of cutting inserts may be offset, in part, by another
cutting flute comprising another series of multiple cutting
inserts. However, if the cutting edges of the flutes, which are
formed by the cutting edges of the multiple individual cutting
inserts comprising the cutting flutes, are not in a true helical
form, the uneven and rough surface topology will never be
completely offset. This problem is even more pronounced with
cutting inserts having sinusoidal or wavelike cutting edges because
the non-linear and non-arcuate cutting edge pattern can create
undulations in a machined surface, particularly when the individual
cutting inserts are out of alignment.
[0039] Solid (i.e., unitary, one-piece) end mills having cutting
edges having sinusoidal or wavelike patterns from one end of the
cutting portion to the other along a perspective helical path may
significantly improve cutting action and increase tool life in
rotary milling applications. Examples of such solid end mills are
described in U.S. Pat. Nos. 4,212,568; 4,560,308; 5,610,232;
7,563,059; and 7,588,396, which are incorporated by reference
herein. However, the unitary construction of these end mills
facilitates the formation of true helical configurations because
there are no indexable or removal parts that create alignment
problems, which prevent the formation of a helical cutting edge on
a multi-insert cutting flute.
[0040] U.S. Pat. Nos. 5,221,164; 5,772,365; and 7,101,122 describe
cutting inserts having wavelike patterns on the individual inserts.
However, the inserts described in these references are not
structurally capable of being assembled into a cutting flute
positioned along and about the length of a cutting tool holder.
Therefore, these inserts cannot form a true helical cutting edge.
U.S. Pat. Nos. 6,773,209 and 6,811,359 describe the problems
encountered on machined surfaces caused by a rotary milling
operation using non-helical cutting tools. These patents describe a
helical cutting system comprising individual cutting inserts having
linear/arcuate cutting edges. However, these patents do not define
the purported helical cutting edge mathematically or quantitatively
and, therefore, do not enable the general design of cutting flutes
comprising indexable inserts and true helical cutting edges.
[0041] As defined in Machinery's Handbook, 26th Edition, Industrial
Press Inc., New York, 2000 (which is incorporated by reference
herein) a helix is a curve generated by a point moving about a
cylindrical surface (real or imaginary) at a constant rate in the
direction of the cylinder's longitudinal axis. Therefore,
geometrically, a helix is a spiral-shaped curve in
three-dimensional space. A helix has the property that a tangent
line at any point along the helix curve has a constant angle with
respect to a fixed line in space. When the fixed line is the
central longitudinal axis of the helix, the constant angle is
defined as the "helix angle." A helix may be defined parametrically
in Cartesian and cylindrical coordinate systems as follows:
TABLE-US-00001 Cartesian coordinates Cylindrical coordinates x(t) =
a cos(t); r(t) = a y(t) = a sin(t); .theta.(t) = t z(t) = bt h(t) =
bt
[0042] In a right-handed Cartesian coordinate system, as the
parameter t increases, the point (x(t), y(t), z(t)) traces a
right-handed helix of radius a and pitch 2.pi.b about the z-axis,
which is parallel and coincident (i.e., co-linear) with the
longitudinal axis of the helix. The pitch of a helix is the length
of one complete helix turn measured parallel to the axis of the
helix. Referring to FIG. 22, a cylindrical helix is shown in which
a=1 and b=1. The helix is shown with increasing parameter t from
t=0 to t=4.pi. (i.e., through two pitches of the helix). In a
cylindrical coordinate system, as the parameter t increases, the
point (r(t), .theta.(t), h(t)) traces a right-handed helix of
radius a and pitch 2.pi.b about the h-axis, which is co-linear with
the longitudinal axis of the helix.
[0043] As used herein, the terms "helix" and "helical" refer to
cylindrical helixes, i.e., helixes having a constant radius about a
central longitudinal axis. A true helical cutting edge may be
defined as a three-dimensional curved cutting edge in which each
point on the cutting edge is located at the same perpendicular
distance to the central longitudinal axis of the rotary cutting
tool (i.e., the cutting axis), within acceptable tolerances. This
perpendicular distance is the cutting radius of the rotary cutting
tool, which is constant along the cutting length of the cutting
tool. Therefore, each point on a helical cutting edge is located on
a conceptual cylindrical surface having a diameter of two times the
cutting radius of the rotary cutting tool.
[0044] A helical cutting edge may be conceptually developed by
moving a point at a constant rate in the longitudinal direction of
the cutting axis and at a constant circumferential rate, while
maintaining a constant distance (equal to the cutting radius) from
the central longitudinal axis (i.e., the cutting axis) of a cutting
tool holder. A cutting edge designed in this manner is a true
helical cutting edge and would not create uneven or rough machined
surface topology, provided that the cutting edge maintains a true
helical shape. This would result in a smooth and accurate cutting
path in rotary machining applications, for example. Further,
combining a sinusoidal curve component with a helical curve
component in a single cutting edge configuration would not prevent
smooth and accurate cutting paths because each point of the cutting
edge would still coincide with the cutting radius.
[0045] The various non-limiting embodiments disclosed and described
in this specification are directed, in part, to cutting inserts
comprising at least one sinusoidal and helical cutting edge, and to
cutting tool systems comprising the inserts, in which the assembly
of the inserts on a tool holder forms a cutting flute comprising a
sinusoidal and helical cutting edge. As used herein, the term
"sinusoidal and helical cutting edge(s)" refers to the cutting edge
portions of a cutting insert that engage a workpiece and cut
material from the workpiece, in which the cutting edges have a
geometric shape comprising a sinusoidal curve component and a
helical curve component. As used herein, the term "sinusoidal and
helical cutting edge(s)" also refers to the cutting edge portions
of a cutting flute comprising an assembly of cutting inserts, in
which the cutting edges of the cutting flute have a geometric shape
comprising a sinusoidal curve component and a helical curve
component.
[0046] Therefore, it is understood that the sinusoidal and helical
cutting edge(s) of a cutting flute are formed by the alignment of
the sinusoidal and helical cutting edge(s) of individual cutting
inserts helically positioned in a tool holder. In addition, it is
understood that the sinusoidal and helical cutting edge(s)
described in this specification comprise a combined sinusoidal and
helical geometric shape within generally acceptable tolerances in
the cutting tool industry.
[0047] The various non-limiting embodiments disclosed and described
in this specification provide the advantage of improved cutting
action and increased tool life that result from sinusoidal cutting
edges. The various non-limiting embodiments disclosed and described
in this specification also provide the advantage of improved
surface finish and more accurate machining path that result from
true helical cutting edges. Further, these advantages are provided
in an indexable cutting tool system in which individual cutting
inserts may be indexed or replaced as necessary due to wear or
failure. Various non-limiting embodiments disclosed and described
in this specification provide a cutting tool system characterized
by a combined sinusoidal and true helical cutting edge, which
improves the rotary machining of difficult-to-machine materials,
such as, for example, titanium and titanium alloys, nickel and
nickel alloys, superalloys, and various exotic metals and metallic
composites.
[0048] The various embodiments disclosed and described in this
specification also provide a design method for producing a cutting
insert comprising at least one indexable, sinusoidal, and helical
cutting edge. This design method creates a mathematical design
model that may be used to manufacture cutting inserts having
sinusoidal and helical cutting edges that together form a cutting
flute having a sinusoidal and helical cutting edge. The various
embodiments disclosed and described in this specification also
provide a design method for positioning multiple cutting inserts in
a tool holder to form a cutting flute comprising a combined
sinusoidal and helical cutting edge in a cutting tool system. This
design method creates a design model that may be used to machine
the insert pockets on a tool holder so that indexable cutting
inserts may be assembled together and aligned to form a cutting
flute comprising a sinusoidal and helical cutting edge.
[0049] FIG. 1 is a three-dimensional perspective view of a cutting
insert 10 comprising two indexable cutting edges 15 and 16, each of
the cutting edges comprising a sinusoidal and helical cutting edge.
The cutting insert 10 includes a center through-hole 11 for
removably securing the cutting insert 10 to a tool holder (not
shown). The sinusoidal and helical cutting edge 15 is located on
the top side 12 of the cutting insert 10. The cutting edge 15
comprises a one-wavelength sinusoidal shape. The cutting edge 15
comprises cutting edges 15a and 15b, which are continuous with each
other and each comprise a half-wavelength sinusoidal shape. The
cutting edge 15 comprises two optional nose corners 15c and 15d
located at the respective ends of the sinusoidal and helical
cutting edge 15.
[0050] The cutting insert 10 also comprises a second cutting edge
16 located on the bottom side 13 of the cutting insert. The cutting
edge 16 comprises a one-wavelength sinusoidal shape. The cutting
edge 16 comprises cutting edges 16a and 16b, which are continuous
with each other and each comprise a half-wavelength sinusoidal
shape. The cutting edge 16 comprises two optional nose corners 16c
and 16d located at the respective ends of the sinusoidal and
helical cutting edge 16.
[0051] The nose corners 15c/15d and 16c/16d are formed from the
initial sharp end points of the sinusoidal and helical cutting
edges 15 and 16, respectively, in order to prevent the ends of the
cutting edges of the insert from being damaged during use in
machining processes. The two sinusoidal and helical cutting edges
15 and 16 of the cutting insert 10 are indexable by rotating the
insert 180-degrees about an axis perpendicular to the axis of the
center through-hole 11 and parallel to the mean line of the
sinusoidal curve component of the cutting edges 15 and 16. This
indexable feature is illustrated in FIGS. 2 and 3.
[0052] FIG. 2 is an end view of the cutting insert 10 shown in FIG.
1 (viewed from the end shown in perspective in FIG. 1). The plane
21 is a middle plane between the top face 12 and the bottom face 13
of the cutting insert 10. The plane 22 is perpendicular to the
middle plane 21 and parallel and aligned with the central axis of
the center through-hole 11. The cutting insert 10 possesses
180-degree rotational symmetry about the axis defined by the
intersection of plane 21 and plane 22. Therefore, the top face 12
and the cutting edge 15 possesses 180-degree rotational symmetry
with respect to the bottom face 13 and cutting edge 16, and as
such, the two sinusoidal and helical cutting edges 15 and 16 of the
cutting insert 10 are indexable by rotating the insert 180-degrees
about the axis defined by the intersection of plane 21 and plane
22.
[0053] FIG. 3 is a top view, together with two detailed views, of
the cutting insert 10 shown in FIGS. 1 and 2 (viewed from the top
face 12 shown in perspective in FIG. 1). The plane 22 is the same
as the plane 22 shown in FIG. 2. As shown on the left-hand side of
FIG. 3, the sinusoidal and helical cutting edge 15 passes through
the points P1, P2, and P3 (in which the points P1 and P3 are
located at the ends of the cutting edge before the formation of the
nose corner 15d at the end point P3 of the cutting edge 15b and the
formation of the nose corner 15c at the end point P1 of the cutting
edge 15a). As shown on the right-hand side of FIG. 3, the
sinusoidal and helical cutting edge 16 passes through the points
P4, P5, and P6 (in which the points P4 and P6 are located at the
ends of the cutting edge before the formation of the nose corner
16d at the end point P6 of the cutting edge 16b and the formation
of the nose corner 16c at the end point P4 of the cutting edge
16a.
[0054] The line 18 is the longitudinal axis of the sinusoidal curve
defining, in part, the cutting edge 15 (i.e., the mean line of the
sinusoidal curve component), wherein the portion 15a and the
portion 15b have the same parameters (i.e., amplitude and
wavelength). The line 19 is the longitudinal axis of the sinusoidal
curve defining, in part, the cutting edge 16 (i.e., the mean line
of the sinusoidal curve component), wherein the portion 16a and the
portion 16b have the same parameters (i.e., amplitude and
wavelength). Although the geometric parameters of portions 15a and
15b of cutting edge 15 are the same as the geometric parameters of
portions 16a and 16b, respectively, of cutting edge 15, it is
understood that in various non-limiting embodiments, these portions
may not necessarily be the same.
[0055] FIG. 4 is a side view of the cutting insert 10 shown in
FIGS. 1-3 (viewed from the left side of the cutting insert as shown
in FIG. 3). FIG. 4 illustrates the orientation of the sinusoidal
and helical cutting edges 15 and 16 relative to the middle plane 21
between the top face 12 and the bottom face 13. The cutting edge 15
has a gradual downward gradient from a high point (relative to
middle plane 21) at the nose corner 15c on the cutting edge portion
15a to a low point (relative to middle place 21) at the nose corner
15d on the cutting edge portion 15b. The gradual downward gradient
of the cutting edge 15 comprises the combined geometric shape of a
sinusoidal curve component and a true helical curve component.
Likewise, the cutting edge 16 has a gradual downward gradient from
a high point (relative to middle plane 21) at the nose corner 16c
on the cutting edge portion 16a to a low point (relative to middle
plane 21) at the nose corner 16d on the cutting edge portion 16b.
The gradual downward gradient of the cutting edge 16 comprises the
combined geometric shape of a sinusoidal curve component and a true
helical curve component.
[0056] FIG. 5(a) is a schematic end view and FIG. 5(b) is a
schematic top view of a cutting insert 50 illustrating the
sinusoidal and helical cutting edges 51 and 52 of the cutting
insert. The cutting insert 50 shown in FIGS. 5(a) and 5(b) is
generally the same as the cutting insert 10 shown in FIGS. 1-4
except that the cutting insert 50 does not have rounded nose
corners, but instead cutting insert 50 has points 56 at the ends of
the sinusoidal and helical cutting edges 51 and 52 of the cutting
insert. The points 56 are shown for the purpose of illustrating the
geometry of the sinusoidal and helical cutting edge 51 (on the top
face 53) and the sinusoidal and helical cutting edge 52 (on the
bottom face 54). The sinusoidal and helical cutting edge 51, for
example, is conceptually produced by trimming a sinusoidal cutting
edge to have a contour that coincides with a helical surface
55.
[0057] The helical surface 55 is geometrically defined to be
coincident with a true helix, as defined above, having a
longitudinal axis 57. The longitudinal axis 57 of the helical
surface 55 forms a helix angle Ha with the center plane 60 of the
cutting insert 50. The helix angle Ha is the same angle as the
constant helix angle formed between a tangent line at any point
along the helix curve (defining the helix surface 55) and the
central longitudinal axis of the helix curve.
[0058] FIG. 6(a) is a top view schematic diagram, and FIGS. 6(b)
and 6(c) are perspective view schematic diagrams, illustrating the
geometric positioning of the cutting insert 50 relative to a
Cartesian coordinate system (XYZ), with the cutting insert
positioned as if it were secured on a rotary tool holder (not
shown). FIG. 6(b) is a perspective end view of the insert 50 as
oriented in FIG. 6(a) (i.e., as viewed along the Y-coordinate
direction as shown in FIG. 6(a)). FIG. 6(c) is a perspective side
view of the insert 50 as oriented in FIG. 6(a) (i.e., as viewed
along the X-coordinate direction as shown in FIG. 6(a)).
[0059] The cutting insert 50 in FIG. 6(a) is shown in an
orientation rotated about the origin O of the XOY plane of the XYZ
coordinate system. The angle of rotation of the insert 50 is equal
to the helix angle Ha of the helical surface 55, which defines the
helical geometric component of the sinusoidal and helical cutting
edge 51. In this manner, the cutting insert 50 is shown in an
orientation as if the cutting insert were positioned on a tool
holder (not shown) having a cutting axis that is co-linear with the
Y-axis of the XYZ coordinate system (see FIG. 21(a)).
[0060] The helical surface 55 is also rotated together with the
cutting insert by the helix angle Ha (that is, the angle between
the center plane 60 of the cutting insert 50 and the Y-axis of the
XYZ coordinate system). In this manner, the angle formed between
the center plane 60 of the cutting insert 50 and the longitudinal
axis of the helix curve defining the helical surface 50 (i.e., the
helical geometric component of the sinusoidal and helical cutting
edge 50) is set equal to the helix angle Ha of the helix curve. As
a result, the helical surface 55 is positioned coincident with a
conceptual cylindrical surface having a central longitudinal axis
co-linear with the cutting axis of a tool holder (not shown) and
having a cylindrical radius equal to the cutting radius R1 of a
cutting tool system comprising a tool holder and the cutting insert
50. FIGS. 6(b) and 6(c) show the positioning of the cutting insert
50 in the XOZ plane and the YOZ plane of the XYZ coordinate system,
respectively, wherein the cutting edge 51 is located within the
helical surface 55 having a helix radius of R1.
[0061] The formation of the sinusoidal and helical cutting edge 51
from P1 to P2 is, therefore, directly associated with the geometric
relationship between the cutting insert 50 and a tool holder (not
shown). This is further illustrated in FIGS. 21(a) and 21(b). FIG.
21(a) is a schematic diagram illustrating the positioning of a
cutting insert 350 (comprising two indexable, sinusoidal, and
helical cutting edges) relative to a tool holder 300 and an XYZ
coordinate system. The cutting insert 350 is generally identical to
the cutting insert 50 shown in FIGS. 5 and 6. The tool holder 300
has a central longitudinal cutting axis 310. The cutting insert 350
is positioned on the tool holder 300 so that the center plane 360
of the cutting insert 350 forms an angle with the axis 310 that is
equal to the helix angle Ha of the helical component of the
sinusoidal and helical cutting edges of the cutting insert.
[0062] FIG. 21(b) is a schematic diagram illustrating the
positioning of a series of common cutting inserts 350, 350', and
350'', each cutting insert comprising two indexable, sinusoidal,
and helical cutting edges, relative to the tool holder 300 and the
XYZ coordinate system. As used herein, the term "common cutting
inserts" and the like means inserts having the same geometric
configuration and dimensions to within generally acceptable
tolerances in the cutting tool industry. For instance, in various
non-limiting embodiments, the common cutting inserts described in
this specification may comprise a series (i.e., a plurality) of
cutting inserts comprising the same material of construction and
having the same shape, cutting features, and dimensions to within
generally acceptable tolerances in the cutting tool industry.
[0063] The common cutting inserts 350, 350', and 350'' are
generally identical to the cutting insert 50 shown in FIGS. 5 and
6, and together the series of common cutting inserts form a cutting
flute comprising the cutting inserts. The cutting flute comprises a
cutting edge having a sinusoidal and helical geometric shape in
which the sinusoidal and helical cutting edge of the cutting flute
is formed by the helical alignment of the individual sinusoidal and
helical cutting edges of the cutting inserts on the tool holder.
The center planes of the cutting inserts 350, 350', and 350'' each
form an angle Ha with the central longitudinal cutting axis 310 of
the tool holder 300. The angle Ha formed between the center planes
of the cutting inserts 350, 350', and 350'' and the central
longitudinal cutting axis 310 of the tool holder 300 is equal to
the helix angle of the helix 370. The helix 370 defines the helical
geometric component of the sinusoidal and helical cutting edges of
the cutting inserts and the combined sinusoidal and helical cutting
edge of the cutting flute formed by the aligned cutting
inserts.
[0064] Referring to FIG. 6, by geometrically defining the
positioning of the cutting insert 50 relative to an XYZ coordinate
system, positioned as if the cutting insert were mounted on a tool
holder, a design method for producing a cutting insert comprising
at least one indexable, sinusoidal, and helical cutting edge may be
used to create a mathematical design model. The mathematical design
model may be used to manufacture cutting inserts having sinusoidal
and helical cutting edges that together form a cutting flute
comprising a sinusoidal and helical cutting edge. The mathematical
design model defines a cutting edge having a three-dimensional
complex geometry comprising a combined sinusoidal curve component
and helical curve component. In accordance with the mathematical
model, every point along a sinusoidal and helical cutting edge
(e.g., cutting edges 51 and 52 in FIG. 6) is located precisely on a
conceptual cylindrical surface (e.g., surface 55 in FIG. 6) defined
by the cutting radius of a cutting tool system comprising a tool
holder (not shown in FIG. 6) and a plurality of common cutting
inserts (e.g., insert 50 in FIG. 6).
[0065] FIGS. 7(a), 7(b), and 7(c) are schematic diagrams
illustrating curves derived to establish a mathematical design
model for the sinusoidal and helical cutting edges of the insert
shown in FIGS. 1-6, in which the curves shown in FIGS. 7(a), 7(b),
and 7(c) correspond to the cutting insert positioning shown in
FIGS. 6(a), 6(b), and 6(c), respectively. In order to establish an
equation for the sinusoidal and helical cutting edge 51, two
dashed-line sinusoidal curves 58 and 59 are introduced, as shown in
FIG. 7(a). The two dashed-line curves 58 and 59 both have the same
geometric shape and dimensions as the cutting edge 51, but have
different orientations relative to the XYZ coordinate system. The
sinusoidal curve 58 has a mean line that is co-linear with the
X-axis of the XYZ coordinate system. The sinusoidal curve 59 is
parallel to the cutting edge 51 and centered on the origin O of the
XYZ coordinate system. The cutting edge 51 may be regarded as a
geometric transformation of the curves 58 and 59, as shown in FIG.
7(a).
[0066] A mathematical equation may be established as follows for
the curve 58 according to the XOY plane of the XYZ coordinate
system in FIG. 7(a), where the Y-axis is co-linear with the cutting
axis of a cutting tool:
Y = B sin ( .pi. A ) X ( 1 ) ##EQU00001##
wherein the parameters B and A are defined in FIG. 7(a) as the
amplitude and half-wavelength of the sinusoidal component of the
cutting edge 51. Equation (1) may be expressed in a general form as
follows:
f.sub.58(X, Y)=0 (2)
Equation (2) generally defines the curve 58 as a function of the X
and Y parameters of the XYZ coordinate system.
[0067] By introducing a rotation transformation (Ro), the following
equation for the curve 59 can be established from the rotation of
the curve 58 about the origin O in the XOY plane of the XYZ
coordinate system:
f 59 ( X , Y ) = f 58 ( X , Y ) Ro = f 58 ( X , Y ) [ cos ( 90
.degree. - Ha ) - sin ( 90 .degree. - Ha ) 0 sin ( 90 .degree. - Ha
) cos ( 90 .degree. - Ha ) 0 0 0 1 ] ( 3 ) ##EQU00002##
wherein Ha is the helix angle as shown in FIG. 6(a), FIG. 7(a), and
FIG. 21(a).
[0068] By introducing a translation transformation (Txy), the
following equation for the cutting edge 51 can be established from
the translation of the curve 59 within the XOY plane:
f 51 ( X , Y ) = f 59 ( X , Y ) Txy = f 59 ( X , Y ) [ 1 0 0 0 1 0
- G cos ( Ha ) G sin ( Ha ) 1 ] ( 4 ) ##EQU00003##
wherein G is defined in FIG. 7(a) as the perpendicular distance
between the mean line of the cutting edge 51 and the mean line of
the curve 59. Ha is the helix angle as described above.
[0069] As shown in FIG. 7(b), in the XOZ plane of the XYZ
coordinate system, the cylindrical surface 55 is defined by the
cutting radius R1 and the entire cutting edge is precisely located
on the cylindrical surface 55. As discussed above, the cylindrical
helix surface 55 shown in FIGS. 6 and 7 is the same as the helical
surface 55 shown in FIG. 5, but rotated with the cutting insert 50
by a helix angle Ha (relative to the XYZ coordinate system) so that
the helical surface 55 becomes a cylindrical surface 55
geometrically related to the cutting radius R1 of a cutting tool
comprising a tool holder and at least one cutting insert 50
comprising a sinusoidal and helical cutting edge 51. Therefore, the
equation of the cylindrical surface 55 in the XOZ plane, as shown
in FIG. 7(b), may be expressed as:
X.sup.2+Z.sup.2=R1.sub.2 (5)
and in a general form as,
f.sub.55(X,Z)=0 (6)
wherein R1 is the radius of the circular cross-section of the
cylindrical surface 55 in the XOZ plane, which is equal to the
cutting radius of a cutting tool with a cutting axis centered at
the origin O and perpendicular to XOZ plane of the XYZ coordinate
system.
[0070] Referring to FIG. 7(b), where the cutting axis is
represented by the Y-axis (perpendicular to the plane of the page),
and is centered at the origin O, every point on the cutting edge 51
from P1 to P2 is located at the cylindrical surface 55 defined by
Equation (5). As noted above, every point on the cutting edge 51
from P1 to P2 is also located on the sinusoidal curve defined by
Equation (4). By extending the sinusoidal curve defined by Equation
(4) (i.e., the sinusoidal component of the cutting edge 51) in the
direction of +/-Z axis to become a three-dimensional sinusoidal
surface perpendicular to the XOY plane, and by simultaneously
extending the circular cross-section defined by Equation (6) (i.e.,
the helical component of the cutting edge 51) in the direction of
+/- Y axis to become a three-dimensional cylindrical surface
perpendicular to the XOZ plane, two three-dimensional equations can
be obtained.
f.sub.51(X,Y,Z)=0 (7)
f.sub.55(X,Y,Z)=0 (8)
[0071] An equation that mathematically defines the
three-dimensional combined sinusoidal and helical cutting edge 51,
as shown in FIG. 6(c) and FIG. 7(c) from P1 to P2, is obtained by
solving Equations (7) and (8) simultaneously to obtain the equation
of a three-dimensional curve defining the intersection of the two
above-described three-dimensional surfaces (i.e., the
three-dimensional sinusoidal surface perpendicular to the XOY plane
and the three-dimensional cylindrical surface perpendicular to the
XOZ plane):
f 51 3 D - C ( X , Y , Z ) = { f 51 ( X , Y , Z ) = 0 f 55 ( X , Y
, Z ) = 0 ( 9 ) ##EQU00004##
where the superscript 3D-C indicates a three-dimensional curve.
[0072] The mathematical design method and resulting design models
described in connection with FIGS. 5-7 and Equations (1)-(9) may be
used to design and fabricate cutting inserts having sinusoidal and
helical cutting edges. The mathematical design model defines a
cutting edge having a three-dimensional complex geometry comprising
a combined sinusoidal curve component and helical curve component.
The method may be summarized as follows.
[0073] First, conceptually positioning the cutting insert as if it
were on a tool holder and forming a helix angle relative to the
longitudinal axis of the tool holder. Second, conceptually rotating
the original helical surface (e.g., surface 55 in FIG. 5) by the
same helix angle. Third, establishing a three-dimensional XYZ
coordinate system with the Y-axis co-linear with the cutting axis
of a cutting tool system defined by a cutting radius that is
centered at the cutting axis (e.g., radius R1 in FIGS. 6 and 7).
Fourth, deriving equations that define the sinusoidal and helical
components of the cutting edge relative to the coordinate system.
In this manner, a helical surface (e.g., surface 55 in FIG. 5) is
converted into a cylindrical surface (e.g., surface 55 in FIGS. 6
and 7) that represents the cutting path defined by the cutting
radius of the cutting tool system, and the sinusoidal surface
intersected by the cylindrical surface mathematically defines a
combined sinusoidal and helical cutting edge.
[0074] The various embodiments disclosed and described in this
specification also provide a design method for positioning multiple
cutting inserts on a tool holder to form a cutting flute comprising
a combined sinusoidal and helical cutting edge in a cutting tool
system. This design method creates a design model that may be used
to machine the insert pockets in a helical orientation on a tool
holder so that indexable cutting inserts may be assembled together
and aligned to form a cutting flute comprising a sinusoidal and
helical cutting edge. This design method is also based on the XYZ
coordinate system established in connection with FIGS. 6-7, and may
be used to specify the assembly of multiple cutting inserts on the
tool holder such that each cutting insert forms a portion of a
sinusoidal and helical cutting edge about the longitudinal cutting
axis.
[0075] FIGS. 8(a) and 8(b) are schematic diagrams illustrating the
relative positioning of a series of common cutting inserts 50 and
62-66, positioned as if the cutting inserts were assembled and
secured to a rotary tool holder (not shown), and helically aligned
to form a cutting flute comprising the series of cutting inserts
and having a cutting edge comprising a sinusoidal and helical
geometric shape. FIG. 8(a) is a schematic view from a direction
perpendicular to the XOY plane of the XYZ coordinate system and
FIG. 8(b) is a schematic view from a direction perpendicular to the
XOZ plane of the XYZ coordinate system. In FIGS. 8(a) and 8(b) the
Y-axis is co-linear with the longitudinal cutting axis of the
cutting tool system.
[0076] As shown in FIG. 8(b), the cylindrical surface 55 is defined
by the cutting radius R1 located at the origin O. The cutting axis
(i.e., the Y-axis) is centered at the origin O and is perpendicular
to the XOZ plane. A first cutting insert 50 having two indexable
sinusoidal and helical cutting edges 51 and 52 is positioned in
accordance with the design method described above. A series of
common cutting inserts 62-66, which are geometrically and
dimensionally the same as the cutting insert 50, are positioned in
helical alignment to form a cutting flute. The sinusoidal and
helical cutting edges of each insert comprising the cutting flute
are in helical alignment and form a combined sinusoidal and helical
cutting edge on the cutting flute.
[0077] In order to position the cutting inserts 62-66 to form a
cutting flute comprising a combined sinusoidal and helical cutting
edge, the cutting inserts may be positioned by: (1) rotating about
the cutting axis (i.e., the Y-axis) while maintaining the constant
cutting radius R1; and (2) translating parallel to the cutting axis
while maintaining the constant cutting radius R1. Any other
positional changes for any of the multiple common cutting inserts
62-66 will cause the cutting inserts to be misaligned and the
cutting edges of the cutting inserts will not lie on the
cylindrical surface 55. Misalignment will create dimensional errors
in the actual cutting path of the cutting tool system (i.e., the
cutting path will not be accurately and precisely defined by the
cutting radius R1). Misalignment will also alter the overall
sinusoidal shape of the cutting edge and invalidate the overall
helical shape of the cutting flute, notwithstanding that each
individual cutting insert has a sinusoidal and helical cutting
edge.
[0078] Geometrically, the position of each cutting insert 62-66 is
initially set at the same position as the cutting insert 50
relative to the XYZ coordinate system, in which the cutting edge 51
is defined by Equation (9). The position of the cutting inserts
62-66 is then mathematically adjusted to an alignment position by
rotating each insert about the cutting axis (i.e., the Y-axis) and
translating each insert parallel to the cutting axis while
maintaining the constant cutting radius. For example, considering
the cutting insert 62, which is positioned immediately adjacent to
the cutting insert 50 and has a cutting edge 72 aligned with the
cutting edge 51 of cutting insert 50, a first movement in the XYZ
coordinate system is a three-dimensional rotation transformation
about the cutting axis (i.e., the Y-axis), and a second movement is
a linear translation transformation parallel to the cutting axis.
The translations from the position of cutting insert 50 to define
the position of cutting insert 72 are derived from Equation (9),
defining the position of cutting insert 50, as follows:
f.sub.72.sup.3D-C(X,Y,Z)=f.sub.51.sup.3D-C(X,Y,Z)Ry(Q)Txyz(J, K, L)
(10)
wherein Ry represents a three-dimensional rotation matrix about the
Y-axis and Txyz represents a three-dimensional translation matrix
parallel to the Y-axis, and the superscript 3D-C indicates a
three-dimensional curve.
[0079] The rotation matrix and the translation matrix are defined
as follows:
Ry ( Q ) = [ cos ( Q ) 0 sin ( Q ) 0 0 1 0 0 - sin ( Q ) 0 cos ( Q
) 0 0 0 0 1 ] ( 11 ) Txyz ( J , K , L ) = [ 1 0 0 0 0 1 0 0 0 0 1 0
J K L 1 ] ( 12 ) ##EQU00005##
wherein Q is the angle of rotation about the Y-axis, and J, K, and
L are the distances moved in each X, Y and Z direction,
respectively. In order to limit the linear movement of the
translation transformation to movement that is parallel to the
Y-axis, J and L are set to zero.
[0080] The remaining cutting inserts 63-66 forming the cutting
flute are the same as the cutting insert 62. Therefore, a general
equation for multiple common cutting inserts, such as, for example,
cutting inserts 62 to 66, may be expressed as indicated in Equation
(13) below, assuming the engaging cutting edge (i.e., the cutting
edge in cutting action) of the first common cutting insert
[f.sub.1.sup.3D-C(X,Y,Z)] is defined and positioned in accordance
with Equations (1) to (9) and the XYZ coordinate system established
in FIGS. 6 to 8:
f.sub.i.sup.3D-C(X,Y,Z)=f.sub.1.sup.3D-C(X,Y,Z)Ry(iQ)T.sub.xyz(J,
iK, L) i=2, . . . , n (13)
wherein i represents the engaging cutting edge for the ith common
cutting insert among a total of n cutting inserts, and
f.sub.i.sup.3D-C(X, Y, Z) represents the position of the engaging
cutting edge of the ith common cutting insert in the XYZ coordinate
system.
[0081] In this manner, the position of each sinusoidal and helical
cutting insert on a tool holder with a defined cutting diameter (or
radius) is mathematically defined so that the overall cutting edge
of the cutting flute formed from the assembly and alignment of the
individual common cutting inserts is a combined sinusoidal and
helical cutting edge, as shown in FIG. 8.
[0082] The mathematical design method and resulting design models
described in connection with FIG. 8 and Equations (10)-(13) may be
used to manufacture cutting tool holders having insert pockets
configured to mechanically engage and secure a series of cutting
inserts having sinusoidal and helical cutting edges so that the
secured inserts are helically aligned to form a cutting flute on
the tool holder and comprising a sinusoidal and helical cutting
edge. The mathematical design model defines the positioning of the
series of cutting inserts so that the cutting edge of the cutting
flute has a three-dimensional complex geometry comprising a
combined sinusoidal curve component and helical curve
component.
[0083] The design methods and models described in this
specification for defining and positioning multiple cutting inserts
on a tool holder are fundamentally different than and distinct from
prior design methods that depend on multiple discrete positional
parameters such as, for example, cutting diameter (or radius),
axial angle, radial angle, and the like. It is not possible to
specify with mathematical accuracy and precision a complex
three-dimensional sinusoidal and helical cutting edge comprising
multiple cutting inserts using prior design methods.
[0084] In various non-limiting embodiments, a method for designing
and/or producing a sinusoidal and helical cutting edge on a cutting
insert comprises:
[0085] (a) positioning a cutting insert having a sinusoidal-shaped
cutting edge as if it were on a tool holder with a helix angle;
and
[0086] (b) modifying the sinusoidal shape of the cutting edge of
the cutting insert to coincide with a cylindrical surface defined
by the cutting radius centered at the cutting axis of a cutting
tool system.
[0087] In various non-limiting embodiments, a method for designing
and/or producing an assembly of common cutting inserts forming a
cutting flute comprising a sinusoidal and helical cutting edge
(wherein each cutting insert comprises at least one sinusoidal and
helical cutting edge) comprises:
[0088] (a) placing a first cutting insert at the position where its
cutting edge is defined in accordance with the above-described
method for designing the sinusoidal and helical cutting edge;
[0089] (b) rotating a second cutting insert (and each subsequent
cutting insert thereafter) about the cutting axis of a cutting tool
system; and
[0090] (c) translating the second cutting insert (and each
subsequent cutting insert thereafter) parallel to the cutting
axis.
[0091] In various non-limiting embodiments, a method for designing
multiple insert pockets to secure multiple common cutting inserts
forming a cutting flute comprising a sinusoidal and helical cutting
edge on a cutting tool holder of a cutting tool system
comprises:
[0092] (a) positioning a seating surface of the first insert pocket
according to the assembly position of the first common cutting
insert having a sinusoidal-shaped cutting edge as if it were on a
tool holder with a helix angle;
[0093] (b) rotating the seating surface of a second insert pocket
(and each subsequent insert pocket thereafter) about the cutting
axis of a cutting tool system; and
[0094] (c) translating the seating surface of the second insert
pocket (and each subsequent insert pocket thereafter) parallel to
the cutting axis while maintaining a constant cutting radius as
defined by the cutting tool system.
[0095] In various non-limiting embodiments, a cutting insert may be
manufactured based on a design model developed using a method for
defining the sinusoidal and helical cutting edge. In various
non-limiting embodiments, a tool holder configured to engage,
secure, and align multiple cutting inserts in multiple respective
insert pockets may be manufactured based on the design model
developed in the method for defining the positioning of cutting
inserts forming a cutting flute comprising a sinusoidal and helical
cutting edge (wherein each cutting insert comprises at least one
sinusoidal and helical cutting edge). For example, cutting inserts
comprising at least one sinusoidal and helical cutting edge may be
fabricated using automated grinding techniques based on the design
model described above in connection with Equations (1)-(9), and
tool holders may be fabricated using computer numerical control
(CNC) machining based on the assembly design model described above
in connection with Equations (10)-(13).
[0096] The cutting inserts manufactured based on the first design
method may be assembled on a tool holder manufactured based in the
second design method to form a cutting tool system. In various
non-limiting embodiments, the cutting tool system may comprise a
tool holder comprising a plurality of common insert pockets
positioned in a helical orientation about a longitudinal axis of
the tool holder. As used herein, the term "common insert pockets"
and the like means a common cutting insert can be secured into any
common insert pocket even though some of the common insert pockets
may be different in geometry. In particular, the common insert
pocket adjacent to the insert pocket of an end-face cutting insert
and the last common insert pocket at the proximal of a cutting
flute (proximal relative to a shank portion of a cutting tool
holder comprising the cutting flute) may have different geometry
but nonetheless be common insert pockets because a common cutting
insert is securable in the respective common insert pockets. The
cutting tool system may also comprise a plurality of common cutting
inserts removably attachable to the plurality of common insert
pockets in the tool holder to form at least one cutting flute on
the tool holder, the at least one cutting flute comprising a
helical grouping of common cutting inserts positioned in the insert
pockets. The common cutting inserts each comprise at least one
sinusoidal and helical cutting edge. The at least one cutting flute
comprises a sinusoidal and helical cutting edge positioned about
the longitudinal axis of the tool holder and formed by alignment of
the individual sinusoidal and helical cutting edges of the common
cutting insert that comprise the at least one cutting flute.
[0097] In various rotary machining applications using cutting tools
comprising multiple indexable cutting inserts, a special front
end-face cutting insert may be advantageous. As used herein, the
term "end-face cutting insert" refers to a cutting insert
configured to be positioned at the front face end of a tool holder
to axially engage a workpiece surface in a direction parallel to
the longitudinal axis of the tool holder. In various non-limiting
embodiments, an end-face cutting insert engages a workpiece surface
both axially and circumferentially, for example, if the end-face
cutting insert is positioned at the periphery of a front end face
of a tool holder. In various non-limiting embodiments, a cutting
tool system comprises an end-face cutting insert configured to at
least axially engage a workpiece during machining operations when
assembled on a tool holder.
[0098] FIGS. 9(a)-9(c) show an end-face cutting insert 80 having
two indexable cutting edges (85 and 86). The end-face cutting
insert 80 is configured to be used as a different end-face cutting
insert in combination with the common cutting inserts shown in FIG.
8 in a cutting tool system comprising sinusoidal and helical
cutting edges.
[0099] As shown in FIG. 9(a), the end-face cutting insert 80
comprises a center through-hole 81 (configured to secure the
cutting insert to a tool holder) and two identical cutting edges 85
and 86. The cutting edges 85 and 86 are located on the top side 82
and the bottom side 83, respectively. The cutting edges 85 and 86
are helical-shaped cutting edges. The two ends of the cutting edge
85 are rounded with nose corners 85a and 85b. The two ends of the
cutting edge 86 are also rounded with nose corners. The end-face
cutting insert 80 is positioned with cutting edge 85 forming an
angle with a cutting axis 84 equal to the helix angle Ha of the
helix curve defining the helical shape of the cutting edge 85.
[0100] FIGS. 10(a) and 10(b) are schematic diagrams illustrating
the relative positioning of a series of common cutting inserts
90-97 and an end-face cutting insert 80, positioned as if the
cutting inserts were assembled and secured to a rotary tool holder
(not shown) to form a cutting flute comprising the series of
cutting inserts and comprising a sinusoidal and helical cutting
edge. The engaging cutting edge 100 of the common cutting insert 90
is defined and positioned in accordance with Equation (9), and the
engaging cutting edges 101-107 of the common cutting inserts 91-97,
respectively, are positioned in accordance with Equation (13).
[0101] The end-face cutting insert 80 is positioned in accordance
with Equation (13) with i=2, but using a different rotating angle Q
and a different translating distance value K because the cutting
edge 85 of the end-face cutting insert 80 is different than the
cutting edges 100-107 of the common cutting inserts 90-97. The
cutting edges 100-107 of the common cutting inserts 90-97 form a
combined sinusoidal and helical cutting edge in the direction of
and about the longitudinal axis of the tool holder (not shown)
(i.e., the Y axis). As shown in FIG. 10(b), all of the cutting
edges 100-107 of the common cutting inserts 90-97, and the cutting
edge 85 of the end-face cutting insert 80, are precisely and
accurately located on the cylindrical surface 99 representing the
cutting diameter/radius of a rotary cutting tool system.
[0102] FIGS. 11(a) and 11(b) are schematic diagrams illustrating
the relative positioning of a series of different-sized end-face
cutting inserts 80, 111, 112, 113, and 114, positioned as if the
end-face cutting inserts where assembled and secured to a rotary
tool holder (not shown) configured to comprise five cutting flutes.
In order to offset any gap between two adjacent cutting inserts in
a cutting flute comprising the cutting inserts (e.g., gaps between
adjacent common cutting inserts or gaps between an end-face cutting
insert and an adjacent common cutting insert), it may be
advantageous to make multiple end-face cutting inserts, each
end-face cutting insert having a different length on the cutting
edge. For example, as shown in FIG. 11(a), the multiple end-face
cutting inserts 80 and 111-114 each have a different length L1-L5,
respectively.
[0103] As shown in FIG. 11(b), each end-face cutting insert has at
least one, and in various non-limiting embodiments, two indexable
cutting edges, that is, cutting edges 85 and 86 of the end-face
cutting insert 80, cutting edges 121 and 122 of the end-face
cutting insert 111, cutting edges 123 and 124 of the end-face
cutting insert 112, cutting edges 125 and 126 of the end-face
cutting insert 113, and cutting edges 127 and 128 of the end-face
cutting insert 114. All of the workpiece-engaging cutting edges
(i.e., cutting edges 85, 121, 123, 125, and 127 of the cutting
inserts 80 and 111-114, respectively) are located on the
cylindrical surface 118 representing the cutting diameter/radius of
a rotary cutting tool system.
[0104] FIGS. 12(a) and 12(b) are schematic diagrams illustrating
the relative positioning of five (5) cutting flutes, each flute
comprising a different-sized end-face cutting insert (80, 111-114),
and a series of common cutting inserts, positioned as if the
cutting inserts were assembled and secured to a rotary tool holder
(not shown). The five (5) cutting flutes each comprise a sinusoidal
and helical cutting edge formed by the assembly and alignment of
the sinusoidal and helical cutting edges of the common cutting
inserts. The end-face cutting inserts (e.g., insert 80) are
positioned and helically aligned with adjacent common cutting
inserts (e.g., insert 90).
[0105] The position of each cutting insert is defined in accordance
with Equation (13), wherein each end-face cutting insert (80,
111-114) may have a set of different values for the Q and K
parameters. All engaging cutting edges, including the helical
cutting edges of the end-face cutting inserts 80 and 111-114, are
located on the cylindrical surface 138 representing the cutting
diameter/radius of a rotary cutting tool system. In various
non-limiting embodiments, it may be advantageous to overlap the
cutting edges in the direction of the longitudinal cutting axis
between the inserts comprising adjacent cutting flutes. Overlapping
cutting edges may improve cutting accuracy and precision because
trailing cutting flutes will remove uncut material left by the
cutting action performed by leading cutting flutes. In this manner,
a plurality of cutting flutes, each flute comprising a helically
aligned assembly of longitudinally offset common cutting inserts,
results in a fully effective cutting flute.
[0106] The amount of residual material left by the cutting action
of a leading cutting flute may be related to the degree of nose
corner rounding of the cutting inserts of the cutting flute. In
various non-limiting embodiments, sinusoidal and helical cutting
inserts comprising rounded nose corners may form small gaps in the
combined sinusoidal and helical cutting edge of the cutting flute
comprising the cutting inserts. A trailing cutting flute comprising
a helically aligned assembly of common cutting inserts that are
longitudinally offset relative to the inserts that comprise a
leading cutting flute will cut and/or remove any residual material
because the rounded nose corners of the inserts comprising the
trailing cutting flute are longitudinally off-set relative to the
nose corners of the inserts comprising the leading cutting flute.
In other words, the junctions between the constituent cutting
inserts of the cutting flutes are not aligned in a plane
perpendicular to the longitudinal cutting axis of a rotary cutting
tool.
[0107] A plurality of cutting flutes, each flute comprising an
aligned assembly of off-set common cutting inserts, is shown in
FIG. 12(b). In various non-limiting embodiments, residual material
left by a leading cutting flute may be cut and/or removed by a
trailing cutting flute because of the off-set established by
end-face cutting inserts that have different shapes and/or
dimensions. For example, end-face cutting inserts 80 and 111-114 in
FIGS. 11 and 12 are commonly-shaped and differently-dimensioned
(i.e., having different lengths L1-L5 as shown in FIG. 11(a)). The
different length cutting edges of the end-face cutting inserts 80
and 111-114 effectively off-set the junctions (and, therefore, any
gaps due to rounded nose corners, or in some cases due to the
geometric constraints of cutting inserts) between adjacent cutting
inserts comprising the cutting flutes.
[0108] In various non-limiting embodiments, it may be desirable for
the cutting inserts comprising each respective cutting flute to
completely overlap (i.e., not be longitudinally off-set) between
each adjacent cutting flute. In other words, the junctions between
the constituent cutting inserts of the cutting flutes are aligned
in a plane perpendicular to the longitudinal cutting axis of a
rotary cutting tool system. By adjusting the values of the Q and K
parameters in Equation (13), an arrangement of the assembly of
common cutting inserts and, optionally, the end-face cutting
inserts, may be defined for a rotary cutting tool system comprising
at least one cutting flute comprising at least one assembly of
common cutting inserts, wherein the individual inserts and the
cutting flute comprise sinusoidal and helical cutting edges.
[0109] FIGS. 13(a) and 13(b) show two views of a cutting tool
system 140 comprising a tool holder 146 and five cutting flutes
141-145, each cutting flute comprising a different-sized end-face
cutting insert (e.g., cutting insert 147a) and a series of common
cutting inserts (e.g., cutting insert 147b), and each cutting flute
141-145 also comprising a sinusoidal and helical cutting edge. The
tool holder 146 comprises five series of common insert pockets
(e.g., insert pocket 148), each series of common insert pockets
positioned in a helical orientation about a longitudinal axis of
the tool holder 146. A plurality of common cutting inserts are
removably attachable to the common insert pockets in the tool
holder 146 to form five cutting flutes 141-145 on the tool holder.
In some embodiments, the insert pockets for the first common
cutting insert (e.g., cutting insert 147c) and the last common
cutting insert (e.g., cutting insert 147d) may be slightly
different in geometry from the rest due to the fact that the first
insert pocket for a first common cutting insert adjoins the insert
pocket for an end-face cutting insert and the last insert pocket
for a last common cutting insert ends at the proximal end of the
flute. The five cutting flutes each comprise a helical grouping of
the common cutting inserts positioned in the insert pockets. The
common cutting inserts each comprise at least one sinusoidal and
helical cutting edge. The five cutting flutes 141-145 each comprise
a sinusoidal and helical cutting edge positioned about the
longitudinal axis of the tool holder 146 and formed by the
alignment of the individual sinusoidal and helical cutting edges of
the common cutting inserts that comprise the five cutting
flutes.
[0110] The five cutting flutes 141-145 shown in FIG. 13(b) each
comprise a different-sized end-face cutting insert having at least
one indexable helical cutting edge. The five cutting flutes 141-145
also comprise multiple common cutting inserts, the cutting inserts
having sinusoidal and helical cutting edges that are aligned to
form the sinusoidal and helical cutting edges of the cutting
flutes. As shown in FIG. 13(a), the workpiece-engaging cutting
edges of the cutting inserts (and, therefore, the cutting edges of
the cutting flutes) are located on the cylindrical surface 149
representing the cutting diameter/radius of the cutting tool
system. As shown in FIG. 13(b), the five different-sized end-face
cutting inserts have a common longitudinal clearance, i.e., extend
beyond the end face of the tool holder 146 by the same distance in
the direction parallel to the longitudinal axis of the tool
holder.
[0111] FIGS. 14(a)-14(c) show three views of a cutting insert 150
comprising four indexable cutting edges 151-154, each cutting edge
comprising a sinusoidal and helical geometric shape. The cutting
insert 150 comprises a center through-hole 155 for mounting and
securing the cutting insert to a tool holder (not shown). The
cutting insert 150 also comprises a top side 156 and a bottom side
157. The four indexable, sinusoidal, and helical cutting edges
151-154 are located on the top side 156 of the cutting insert 150.
The cutting insert 150 possesses 90-degree rotational symmetry
about the central axis of the through-hole 155.
[0112] The four sinusoidal and helical cutting edges 151-154 of the
cutting insert 150 are indexable by rotating the insert 90-degrees
about the central axis of the through-hole 155. As shown in FIG.
14(b), the cutting edge 151 from point N1 through N2 to N3 is a
one-wavelength sinusoidal curve, wherein line 158 is the
longitudinal mean line axis of the sinusoidal curve, and the line
159 is the vertical axis of the sinusoidal curve. In some
embodiments, the existing sinusoidal cutting edge 151 shown in FIG.
14 may be in an alternative shape being mirrored via the
longitudinal mean line 158, that is, a sinusoidal cutting edge with
its sole peak point positioned along the vertical line 159 but
above the longitudinal line 158 of sinusoidal the curve.
[0113] FIGS. 15(a)-15(c) are schematic diagrams illustrating the
geometric positioning of the cutting insert 150 relative to an XYZ
coordinate system as if the cutting insert were secured to a rotary
tool holder (not shown). FIG. 15(a) is a side view schematic
diagram of the cutting insert 150 as positioned on the tool holder
with the longitudinal axis 164 of the sinusoidal cutting edge 151
forming a helix angle Ha with the longitudinal cutting axis 163 of
a cutting tool system, which is co-linear with the Y-axis of the
XYZ coordinate system. FIG. 15(c) is a perspective view schematic
diagram of the cutting insert 150 as viewed along the direction of
the Y-axis (i.e., along the cutting axis 163) as shown in FIG.
15(a). FIG. 15(c) illustrates that the entire sinusoidal and
helical cutting edge 151 is located on the cylindrical surface 166
defined by the cutting radius R4, wherein the cutting axis 163 is
centered at the origin O in FIG. 15(c). Therefore, the sinusoidal
and helical cutting edges 151-154 of the cutting insert 150 produce
an accurate cutting path defined by the cutting radius R4 centered
at the cutting axis 163. The design model and equations that define
the sinusoidal and helical cutting edges 151-154 of the cutting
insert 150 are developed using the same design method described
above in connection with Equations (1)-(9).
[0114] FIGS. 16(a) and 16(b) are schematic diagrams illustrating
the relative positioning of a series of common cutting inserts 150
and 171-175, positioned as if the cutting inserts were assembled
and secured to a rotary tool holder (not shown) to form a cutting
flute 170 comprising the series of common cutting inserts and
comprising a sinusoidal and helical cutting edge formed by the
aligned sinusoidal and helical cutting edges of the series of
common cutting inserts. The common cutting inserts 150 and 171-175
each comprise four indexable, sinusoidal, and helical cutting edges
(e.g., cutting edges 151 and 181-185 on cutting inserts 150 and
171-175, respectively). Although a different end-face cutting
insert is not shown in FIG. 16, it is understood that the
embodiment illustrated in FIG. 16 may further comprise a different
end-face cutting insert. The design model and equations that define
the positioning of the cutting inserts 150 and 171-175 to form a
cutting flute comprising a sinusoidal and helical cutting edge
formed by the indexable, sinusoidal, and helical cutting edges 151
and 181-185 (including the positioning of a different end-face
cutting insert, not shown) are developed using the same design
method described above in connection with Equations (10)-(13).
[0115] The longitudinal cutting axis 177 of the rotary cutting tool
system comprising the cutting inserts 150 and 171-175 is co-linear
with the Y-axis of the XYZ coordinate system. The sinusoidal and
helical cutting edge of the cutting flute 170 formed from the
aligned cutting edges 151 and 181-185 of the individual cutting
inserts 150 and 171-175, respectively, includes gaps between the
adjacent cutting inserts that comprise the cutting flute. For
example, a gap labeled Ygap in FIG. 16(a) is shown between the
cutting edges 182 and 183 of cutting inserts 172 and 173,
respectively, of the cutting flute 170. As shown in FIG. 16(b),
notwithstanding the gap between adjacent cutting inserts, the
workpiece-engaging cutting edges 151 and 181-185, which form the
sinusoidal and helical cutting edge of the cutting flute 170, are
located on the cylindrical surface 178 defined by a cutting radius
R4 centered at the origin O, wherein the cutting axis 177 is also
centered at the origin O.
[0116] The gap between the adjacent cutting inserts of a cutting
flute may be compensated for by longitudinally offsetting the
cutting inserts relative to adjacent cutting flutes, as described
above. For example, a trailing cutting flute comprising an assembly
of common cutting inserts may be longitudinally offset along the
Y-axis relative to a leading cutting flute. In other words, the
gaps between the constituent cutting inserts of the cutting flutes
are not aligned in a plane perpendicular to the longitudinal
cutting axis of a rotary cutting tool system comprising the cutting
flutes.
[0117] FIGS. 17(a) and 17(b) are schematic diagrams illustrating
the relative positioning of a common cutting insert 191 having two
indexable cutting edges 195 and 196, and a different end-face
cutting insert 192 having two indexable cutting edges 197 and 198,
positioned as if the cutting inserts were assembled and secured to
a rotary tool holder (not shown) to form a cutting flute 190
comprising the cutting inserts and also forming a cutting edge
having a sinusoidal and helical geometric shape. The cutting edges
195-198 are sinusoidal and helical cutting edges. The
workpiece-engaging cutting edge 195 of the common cutting insert
190 is defined and positioned using a design model derived using
the design method described above in connection with Equations
(1)-(9). The cutting inserts are positioned to form a cutting flute
comprising a sinusoidal and helical cutting edge using a design
model derived using the design method described above in connection
with Equations (10)-(13). As shown in FIG. 17(a), the work-piece
engaging cutting edges 197 and 195, which form the sinusoidal and
helical cutting edge of the cutting flute 190, are located on the
cylindrical surface 194 defined by a cutting radius R2 centered at
the origin O, wherein the longitudinal cutting axis 193 is also
centered at the origin O.
[0118] FIGS. 18(a) and 18(b) are two views of a cutting insert 200
comprising two indexable cutting edges 201 and 202, each cutting
edge having a sinusoidal and helical geometric shape. The cutting
insert 200 comprises two through-holes 204 and 205 for securing the
cutting insert to a tool holder (not shown). As shown in FIG.
18(b), the cutting edge 201 from point G1 through G2 to G3
comprises a one-wavelength sinusoidal curve in which line 206 is
the longitudinal mean line axis of the sinusoidal curve, and the
line 207 is the vertical axis of the sinusoidal curve. As shown in
FIG. 18(a), the sinusoidal curve passing through points G1, G2, and
G3 follows a helical surface 208 on the top side 209 of the cutting
insert 200.
[0119] FIGS. 19(a) and 19(b) show two views of a cutting insert 210
comprising two indexable cutting edges 211 and 212, each cutting
edge having a sinusoidal and helical shape. The cutting insert 210
comprises a center through-hole 215 for securing the cutting insert
to a tool holder (not shown). As shown in FIG. 19(b), the cutting
edge 210 from point H1 through H2 to H3 comprises a one-wavelength
sinusoidal curve in which line 216 is the longitudinal mean line
axis of the sinusoidal curve, and the line 217 is the vertical axis
of the sinusoidal curve. As shown in FIG. 19(a), the sinusoidal
curve passing through points H1, H2, and H3 follows a helical
surface 218 on the top side 219 of the cutting insert 210.
[0120] FIG. 20 is a three-dimensional perspective view of a cutting
insert 220 (similar to the cutting insert shown in FIGS. 1-6 and 8)
comprising two indexable, sinusoidal, and helical cutting edges 221
and 22, and further comprising notches 227 and 228 positioned along
the cutting edges 221 and 222, respectively. The cutting insert 220
comprises a center through-hole 225 for securing the insert to a
tool holder (not shown). The cutting edge 221 is located on the top
side 223 of the cutting insert 220 and comprises cutting edges 221a
and 221b, and nose corners 221c and 221d. The cutting edge 222 is
located on the bottom side 224 of the cutting insert 220 and
comprises cutting edges 222a and 222b, and nose corners 222c and
222d.
[0121] The nose corners 221c/221d and 222c/222d are formed from the
initial sharp end points of the sinusoidal and helical cutting
edges 221 and 222, respectively, in order to prevent the ends of
the cutting edges of the cutting insert from being damaged during
use in machining processes. The two sinusoidal and helical cutting
edges 221 and 222 of the cutting insert 220 are indexable by
rotating the insert 180-degrees about an axis perpendicular to the
axis of the center through-hole 225 and parallel to the mean line
of the sinusoidal curves of the cutting edges 221 and 222.
[0122] The notches 227 positioned along the cutting edge 221, and
the notches 228 positioned along the cutting edge 222, may be in
any geometric form or shape. In various non-limiting embodiments,
the number of notches positioned in a cutting edge may be at least
one, and in some embodiments, may range from 1 to 10 per cutting
edge. In various non-limiting embodiments, notches may be uniformly
distributed along a cutting edge or non-uniformly distributed along
a cutting edge.
[0123] In various non-limiting embodiments, a cutting tool system
comprises a tool holder and a plurality of common cutting inserts.
The tool holder comprises a plurality of common insert pockets
positioned in a helical orientation about a longitudinal axis of
the tool holder. The plurality of common cutting inserts are
removably attachable to the plurality of common insert pockets in
the tool holder. When so attached, the plurality of common cutting
inserts form at least one cutting flute on the tool holder. The at
least one cutting flute comprises a helical grouping of common
cutting inserts positioned in the insert pockets. The common
cutting inserts each comprise at least one sinusoidal and helical
cutting edge. The at least one cutting flute comprises a sinusoidal
and helical cutting edge positioned about the longitudinal axis of
the tool holder. The sinusoidal and helical cutting edge of the
cutting flute is formed by alignment of the individual sinusoidal
and helical cutting edges of the common cutting inserts that
comprise the at least one cutting flute.
[0124] In various non-limiting embodiments, a cutting tool system
comprises a tool holder and a plurality of common cutting inserts.
The tool holder comprises two or more series of common insert
pockets. Each series of common insert pockets are positioned in a
helical orientation about a longitudinal axis of the tool holder.
The plurality of common cutting inserts are removably attachable to
the common insert pockets in the tool holder. When so attached, the
plurality of common cutting inserts form two or more cutting flutes
on the tool holder. The two or more cutting flutes each comprise a
helical grouping of the common cutting inserts positioned in the
insert pockets. The common cutting inserts each comprise at least
one sinusoidal and helical cutting edge. The two or more cutting
flutes each comprise a sinusoidal and helical cutting edge
positioned about the longitudinal axis of the tool holder. The
sinusoidal and helical cutting edge of the cutting flute is formed
by alignment of the individual sinusoidal and helical cutting edges
of the common cutting inserts that comprise the two or more cutting
flutes.
[0125] In various non-limiting embodiments, at least one sinusoidal
and helical cutting edge of a common cutting insert may comprise a
shape of one sinusoidal wavelength. In various non-limiting
embodiments, a cutting insert may comprise two or more sinusoidal
and helical cutting edges that are indexable in insert pockets in a
tool holder, such as, for example, comprising two sinusoidal and
helical cutting edges or four (4) sinusoidal and helical cutting
edges that are indexable in the insert pockets.
[0126] In various non-limiting embodiments, a cutting tool system
may also comprise an end-face cutting insert removably attachable
to an insert pocket positioned at an engaging end of a tool holder,
the end-face cutting insert having a shape that is different than a
shape of a plurality of common cutting inserts. In various
non-limiting embodiments, an end-face cutting insert may comprise a
helical cutting edge that helically aligns with the sinusoidal and
helical cutting edges of a plurality of common cutting inserts that
form the sinusoidal and helical cutting edge of at least one
cutting flute. In various non-limiting embodiments, an end-face
cutting insert may comprise a sinusoidal and helical cutting edge
that helically aligns with the sinusoidal and helical cutting edges
of a plurality of common cutting inserts that form the sinusoidal
and helical cutting edge of at least one cutting flute.
[0127] In various non-limiting embodiments, a cutting tool system
may comprise adjacent helical groupings of common cutting inserts
that are offset relative to each other along the longitudinal axis
of a tool holder so that the inserts comprising adjacent helical
cutting flutes are not longitudinally aligned in a cross sectional
plane perpendicular to the longitudinal axis. In various
non-limiting embodiments, a cutting tool system may comprise two or
more differently-sized end-face cutting inserts that are positioned
in respective insert pockets with a common longitudinal clearance,
so that adjacent helical groupings of the common cutting inserts
are offset relative to each other along the longitudinal axis of
the tool holder so that the inserts comprising adjacent helical
flutes are not longitudinally aligned in a cross sectional plane
perpendicular to the longitudinal axis.
[0128] The non-limiting embodiments described in this specification
are directed to cutting inserts and cutting tool systems comprising
sinusoidal and helical cutting edges. The embodiments described in
this specification provide various advantages including, for
example, improved cutting action and increased tool life as a
result of sinusoidal cutting edge geometry, and improved machined
surface finish and machining path accuracy as a result of helical
cutting edge geometry. The cutting inserts described herein
comprising a sinusoidal and helical cutting edge may be
manufactured in various sizes and shapes, and configured for use in
a variety of rotary machining applications. It is understood that
cutting inserts produced in accordance with the embodiments
described herein may include acceptable manufacturing tolerances in
terms of size, shape, and other geometric parameters.
[0129] This specification has been written with reference to
various non-limiting and non-exhaustive embodiments. However, it
will be recognized by persons having ordinary skill in the art that
various substitutions, modifications, or combinations of any of the
disclosed embodiments (or portions thereof) may be made within the
scope of this specification. For instance, the cutting tool system
disclosed in this specification comprising a plurality of common
cutting inserts forming at least one sinusoidal and helical cutting
edge may be designed to have differential helix, differential pitch
or non equi-spaced cutting flutes, and the cutting inserts
presented in this invention may have non-standard sinusoidal wave
patterns, and correspondingly, there may be a second group of
common cutting inserts that are different in geometry from the
first group of common cutting inserts. Thus, it is contemplated and
understood that this specification supports additional embodiments
not expressly set forth herein. Such embodiments may be obtained,
for example, by combining, modifying, or reorganizing any of the
disclosed steps, components, elements, features, aspects,
characteristics, limitations, and the like, of the various
non-limiting embodiments described in this specification. In this
manner, Applicants reserve the right to amend the claims during
prosecution to add features as variously described in this
specification, and such amendments comply with the requirements of
35 U.S.C. .sctn.112, first paragraph, and 35 U.S.C.
.sctn.132(a).
* * * * *